The difference in Cuomo's popularity between homes with gun owners and those without was stark. There also was a major difference between those who live in upstate New York and those in the New York City area.

Voters in non-gun homes approved of the Democratic governor 68 percent to 19 percent. Voters in households with a gun disapproved of him 50 percent to 40 percent, the poll said.

In upstate, Cuomo's approval rating was 51 percent, compared with 66 percent in New York City and 64 percent in the New York City suburbs.

Cuomo's standing among Republicans took the largest hit. Republicans' approval of Cuomo fell from 68 percent to 44 percent, the poll said.

"Is Gov. Cuomo's honeymoon with Republicans over, or is this just a spat that can be patched up in the months ahead?' Maurice Carroll, Quinnipiac's pollster, said in a statement. "Cuomo lost some Republican support after the 2011 same-sex marriage bill, but he got it back."

Carroll later told reporters that Cuomo's drop appeared to be indicative of a perceived shift toward more liberal policies in his State of the State address Jan. 9. In addition to outlining his gun proposal in the speech, Cuomo talked about wanting to expand women's reproductive health rights and increasing the minimum wage.

"Gun control, sure, it's obviously an issue," Carroll said. "But also he meandered over the whole liberal landscape in that very peculiar State of the State speech."

Cuomo indicated earlier this week that he expected his poll numbers to drop after the controversial gun law was passed Jan. 15. He said Wednesday he wasn't surprised by the Quinnipiac poll.

"We are not here to duck the tough issues. We are here to take on the tough issues," Cuomo told reporters at the Capitol after a meeting with legislative leaders. "I said to my colleagues, they elect us to lead and they elect us to solve the problems that have dogged this state and this society for many, many years."

The state Rifle and Pistol Association said Tuesday it will soon file a lawsuit against the state over the law, and Cuomo said the lawsuit was also expected. He predicted the law would withstand a court challenge.

Cuomo said gun owners would be more comfortable with the law once they better understand it and realize the state is not targeting law-abiding gun owners.

The poll found voters split on whether the law went too far in restricting gun-owners' rights. Fifty-one percent of upstate voters said the gun law went too far, while only 28 percent of suburban New York City residents said it did.

"The more that they understand the law and the more they hear about the law, the better they are going to feel because it has nothing to do with the legitimate ownership of a gun," Cuomo continued.

Gun-rights groups have expressed concern that by owning legal guns, such as assault weapons, they will be in violation of the law. Gun owners have a year to register their guns as part of the law's tougher ban on assault weapons.

Cuomo said all that is required is filling out a card to register any assault weapons that are still legal under the law.

"If you have an assault rifle, which we believe is extraordinarily dangerous in the wrong hands, you have it, you own it, you register it if you want to keep it. People register handguns all the time," Cuomo explained.

From Jan. 23-28, Quinnipiac surveyed 1,127 New York voters. The poll had a margin of error of 2.9 percentage points.